Hey gang,(adsbygoogle = window.adsbygoogle || []).push({});

I'm re-working my way through gauge theory, and I've what may be a silly question.

Promotion of global to local symmetries in order to 'reveal' gauge fields (i.e. local phase invariance + Dirac equation -> EM gauge field) is, as far as i can tell, always done on the Lagrangian, as the Lagrangian must be invariant under the symmetry imposed.

My question is: does this necessarily imply that the equation of motion is always invariant? If so, is the procedure of trying to find an invariant equation of motion equivalent? Is it just that due to the churning of the Lagrangian through the Euler Lagrange equations, the EoM is usually more complicated and so harder to see easy ways to make things invariant under certain operations?

Thanks,

-FD

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# Local gauge symmetries Lagrangians and equations of motion

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